Having cruised to a 3-0 win in the first leg, Arsenal appeared complacent in the first half.
Ostersunds made use of the opportunity and scored two goals in the first half, raising hopes of a sensational comeback. However, Sead Kolasinac’s goal for Arsenal in the second half helped the home side win 4-2 on aggregate.
“We were nowhere near it and not good enough,” Arsenal midfielder Jack Wilshere said.
“We are through and that is all that counts. We will see who we get tomorrow and refocus on the big game on Sunday,” he added, referring to Sunday’s League Cup final against Manchester City.
Thursday’s Europa League action was marred by violent clashes at the match between Athletic Bilbao and Spartak Moscow which left one police officer dead.
Bilbao lost 2-1 but still qualified to the round of 16 on a 4-3 aggregate.
Marcel Schmelzer scored a late equaliser for Borussia Dortmund that helped them beat Atalanta on a 4-3 aggregate.
Serie A leaders Napoli put up a spirited fight to win 2-0 against RB Leipzig in the second leg. However, that wasn’t enough to overturn the 3-1 loss in the first leg as the Serie A leaders exited the championship on away goals.
Meanwhile, the draw for the round of 16 was announced today with Arsenal facing seven-time European champions AC Milan.
Atletico Madrid face Lokomotiv Moscow while Athletic Bilbao were paired with Marseille for the matches on March 8 and March 15.